Silva found the bottom left corner for the first-half opener before converting a penalty after the break to send his manager home happy on a miserable night for Roberto Martinez and his new team.
The away side should really have won by a bigger margin, while the hosts, who were outplayed and rarely threatened to score, were booed on numerous occasions by the frustrated Brussels crowd.
"We're happier with the account the lads gave of themselves than the result. It was a good performance," said Spain coach Julen Lopetegui.
The ex-FC Porto boss, who was appointed as Vicente del Bosque's replacement in July, continued: "The players showed a real willingness to work for the team, and the effect of that was clear to see. I think they enjoyed themselves."